IEICE TRANSACTIONS on Electronics
An Efficient Reconstruction Algorithm for Diffraction Tomography
Summary :
An efficient reconstruction algorithm for diffraction tomography based on the modified Newton-Kantorovich method is presented and numerically studies. With the Fréchet derivative obtained for the Helmholtz equation, one can derive an iterative formula for getting an object function, which is a function of refractive index of a scatterer. Setting an initial guess of the object function to zero, the pth estimate of the function is obtained by performing the inverse Fourier transform of its spectrum. Since the spectrum is bandlimited within a low-frequency band, the algorithm does not require usual regularization techniques to circumvent ill-posedness of the problem. For numerical calculation of the direct scattering problem, the moment method and the FFT-CG method are utilized. Computer simulations are made for lossless and homogeneous dielectric circular cylinders of various radii and refractive indices. In the iteration process of image reconstruction, the imaginary part of the object function is set to zero with a priori knowledge of the lossless scatterer. Then the convergence behavior of the algorithm remarkably gets improved. From the simulated results, it is seen that the algorithm provides high-quality reconstructed images even for cases where the first-order Born approximation breaks down. Furthermore, the results demonstrate fast convergence properties of the iterative procedure. In particular, we can successfully reconstruct the cylinder of radius 1 wavelength and refractive index that differs by 10% from the surrounding medium. The proposed algorithm is also effective for an object of larger radius.
- Publication
- IEICE TRANSACTIONS on Electronics Vol.E75-C No.11 pp.1387-1394
- Publication Date
- 1992/11/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Electromagnetic Theory
Authors
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Haruyuki HARADA, Takashi TAKENAKA, Mitsuru TANAKA, "An Efficient Reconstruction Algorithm for Diffraction Tomography" in IEICE TRANSACTIONS on Electronics,
vol. E75-C, no. 11, pp. 1387-1394, November 1992, doi: .
Abstract: An efficient reconstruction algorithm for diffraction tomography based on the modified Newton-Kantorovich method is presented and numerically studies. With the Fréchet derivative obtained for the Helmholtz equation, one can derive an iterative formula for getting an object function, which is a function of refractive index of a scatterer. Setting an initial guess of the object function to zero, the pth estimate of the function is obtained by performing the inverse Fourier transform of its spectrum. Since the spectrum is bandlimited within a low-frequency band, the algorithm does not require usual regularization techniques to circumvent ill-posedness of the problem. For numerical calculation of the direct scattering problem, the moment method and the FFT-CG method are utilized. Computer simulations are made for lossless and homogeneous dielectric circular cylinders of various radii and refractive indices. In the iteration process of image reconstruction, the imaginary part of the object function is set to zero with a priori knowledge of the lossless scatterer. Then the convergence behavior of the algorithm remarkably gets improved. From the simulated results, it is seen that the algorithm provides high-quality reconstructed images even for cases where the first-order Born approximation breaks down. Furthermore, the results demonstrate fast convergence properties of the iterative procedure. In particular, we can successfully reconstruct the cylinder of radius 1 wavelength and refractive index that differs by 10% from the surrounding medium. The proposed algorithm is also effective for an object of larger radius.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e75-c_11_1387/_p
Copy
@ARTICLE{e75-c_11_1387,
author={Haruyuki HARADA, Takashi TAKENAKA, Mitsuru TANAKA, },
journal={IEICE TRANSACTIONS on Electronics},
title={An Efficient Reconstruction Algorithm for Diffraction Tomography},
year={1992},
volume={E75-C},
number={11},
pages={1387-1394},
abstract={An efficient reconstruction algorithm for diffraction tomography based on the modified Newton-Kantorovich method is presented and numerically studies. With the Fréchet derivative obtained for the Helmholtz equation, one can derive an iterative formula for getting an object function, which is a function of refractive index of a scatterer. Setting an initial guess of the object function to zero, the pth estimate of the function is obtained by performing the inverse Fourier transform of its spectrum. Since the spectrum is bandlimited within a low-frequency band, the algorithm does not require usual regularization techniques to circumvent ill-posedness of the problem. For numerical calculation of the direct scattering problem, the moment method and the FFT-CG method are utilized. Computer simulations are made for lossless and homogeneous dielectric circular cylinders of various radii and refractive indices. In the iteration process of image reconstruction, the imaginary part of the object function is set to zero with a priori knowledge of the lossless scatterer. Then the convergence behavior of the algorithm remarkably gets improved. From the simulated results, it is seen that the algorithm provides high-quality reconstructed images even for cases where the first-order Born approximation breaks down. Furthermore, the results demonstrate fast convergence properties of the iterative procedure. In particular, we can successfully reconstruct the cylinder of radius 1 wavelength and refractive index that differs by 10% from the surrounding medium. The proposed algorithm is also effective for an object of larger radius.},
keywords={},
doi={},
ISSN={},
month={November},}
Copy
TY - JOUR
TI - An Efficient Reconstruction Algorithm for Diffraction Tomography
T2 - IEICE TRANSACTIONS on Electronics
SP - 1387
EP - 1394
AU - Haruyuki HARADA
AU - Takashi TAKENAKA
AU - Mitsuru TANAKA
PY - 1992
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E75-C
IS - 11
JA - IEICE TRANSACTIONS on Electronics
Y1 - November 1992
AB - An efficient reconstruction algorithm for diffraction tomography based on the modified Newton-Kantorovich method is presented and numerically studies. With the Fréchet derivative obtained for the Helmholtz equation, one can derive an iterative formula for getting an object function, which is a function of refractive index of a scatterer. Setting an initial guess of the object function to zero, the pth estimate of the function is obtained by performing the inverse Fourier transform of its spectrum. Since the spectrum is bandlimited within a low-frequency band, the algorithm does not require usual regularization techniques to circumvent ill-posedness of the problem. For numerical calculation of the direct scattering problem, the moment method and the FFT-CG method are utilized. Computer simulations are made for lossless and homogeneous dielectric circular cylinders of various radii and refractive indices. In the iteration process of image reconstruction, the imaginary part of the object function is set to zero with a priori knowledge of the lossless scatterer. Then the convergence behavior of the algorithm remarkably gets improved. From the simulated results, it is seen that the algorithm provides high-quality reconstructed images even for cases where the first-order Born approximation breaks down. Furthermore, the results demonstrate fast convergence properties of the iterative procedure. In particular, we can successfully reconstruct the cylinder of radius 1 wavelength and refractive index that differs by 10% from the surrounding medium. The proposed algorithm is also effective for an object of larger radius.
ER -
English
